Given:
m = 1160 kg
g = 9,81 m/s²
v = 2.5 m/s
Unknown:
k spring constant
x spring compression
1. equation to use is Newton's 2nd law and Hook's law:

2. equation to use, the energy of the spring must equal the energy of the satellite:

Combinig the two equations:
Answer:
The vertical distance is ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
Explanation:
From the question we are told that
The mass of the cylinder is m
The kinetic frictional force is f
Generally from the work energy theorem

Here E the the energy of the spring which is increasing and this is mathematically represented as

Here k is the spring constant
P is the potential energy of the cylinder which is mathematically represented as

And
is the workdone by friction which is mathematically represented as

So

=> ![\frac{1}{2} * k * d^2 = d[mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%5E2%20%3D%20%20d%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![\frac{1}{2} * k * d = [mg + f ]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20k%20%20%2A%20%20d%20%3D%20%20%5Bmg%20%2B%20%20f%20%20%20%20%5D)
=> ![d = \frac{2}{k} *[mg + f]](https://tex.z-dn.net/?f=d%20%3D%20%5Cfrac%7B2%7D%7Bk%7D%20%2A%5Bmg%20%2B%20f%5D)
1) 
When both the electric field and the magnetic field are acting on the electron normal to the beam and normal to each other, the electric force and the magnetic force on the electron have opposite directions: in order to produce no deflection on the electron beam, the two forces must be equal in magnitude

where
q is the electron charge
E is the magnitude of the electric field
v is the electron speed
B is the magnitude of the magnetic field
Solving the formula for v, we find

2) 4.1 mm
When the electric field is removed, only the magnetic force acts on the electron, providing the centripetal force that keeps the electron in a circular path:

where m is the mass of the electron and r is the radius of the trajectory. Solving the formula for r, we find

3) 
The speed of the electron in the circular trajectory is equal to the ratio between the circumference of the orbit,
, and the period, T:

Solving the equation for T and using the results found in 1) and 2), we find the period of the orbit:

Answer:

Explanation:
We know that speed is given by dividing distance by time or multiplying length and frequency. The speed of the father will be given by Lf where L is the length of the father’s leg ad f is the frequency.
We know that frequency of simple pendulum follows that 
Now, the speed of the father will be
while for the child the speed will be 
The ratio of the father’s speed to the child’s speed will be
